Nonlinear Dynamics and Turbulence Group, IST Austria, 3400 Klosterneuburg, Austria.
Freeside LLC, 3344 Peachtree Rd., Atlanta, Georgia 30326, USA.
Chaos. 2019 Jan;29(1):013122. doi: 10.1063/1.5058279.
We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application of dynamical systems theory tools. As an illustration of the utility of the symmetry reduction, we apply it to a model of the pilot-wave system with a central harmonic force. We begin our analysis by identifying local bifurcations and the onset of chaos. We then describe the emergence of chaotic regions and their merging bifurcations, which lead to the formation of a global attractor. In this final regime, the droplet's angular momentum spontaneously changes its sign as observed in the experiments of Perrard et al. [Phys. Rev. Lett.113(10), 104101 (2014)].
我们考虑在存在中心势的情况下，一个液滴在同一种流体的振动浴中的运动。我们制定了一个旋转对称性降低的系统描述，这使得动力系统理论工具的直接应用成为可能。作为对称约简的实用性的说明，我们将其应用于具有中心调和力的导波系统模型。我们首先通过识别局部分叉和混沌的出现来开始我们的分析。然后，我们描述了混沌区域的出现及其合并分叉，这导致了全局吸引子的形成。在这个最终的状态下，液滴的角动量会像 Perrard 等人的实验中观察到的那样自发地改变其符号。[Phys. Rev. Lett.113(10), 104101 (2014)]。
